Reconstruction of the one‐particle density matrix from expectation values in position and momentum space

1992 ◽  
Vol 96 (12) ◽  
pp. 8986-8994 ◽  
Author(s):  
Hartmut Schmider ◽  
Vedene H. Smith ◽  
Wolf Weyrich
Keyword(s):  
Density Matrix ◽  
Momentum Space ◽  
Particle Density ◽  
Expectation Values ◽  
The One

On the Inference of the One-Particle Density Matrix from Position and Momentum-Space Form Factors

1993 ◽  
Vol 48 (1-2) ◽  
pp. 211-220
Author(s):  
Hartmut Schmider ◽  
Vedene H. Smith, Jr. ◽  
Wolf Weyrich
Keyword(s):  
Density Matrix ◽  
Electron Correlation ◽  
Momentum Space ◽  
Space Form ◽  
Particle Density ◽  
Form Factors ◽  
Reduced Density Matrix ◽  
Expectation Values ◽  
The One ◽  
Reduced Density

Abstract A modification of a recently developed method for the least-squares reconstruction of a one-particle reduced density matrix from experimentally accessible expectation values is applied to the test systems of atomic beryllium and neon. The improvement of the resulting matrices through inclusion of electron correlation is demonstrated. Their quality is judged by comparison of the moments of the position and momentum densities and of the spherically averaged density matrix in a suitable representation.

Density cumulant functional theory: The DC-12 method, an improved description of the one-particle density matrix

2013 ◽  
Vol 138 (2) ◽  
pp. 024107 ◽  
Author(s):  
Alexander Yu. Sokolov ◽  
Andrew C. Simmonett ◽  
Henry F. Schaefer
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Functional Theory ◽  
The One

scholarly journals The Energy-Density Functional of an Electron Gas in Locally Linear Approximation of the One-Body Potential

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1176-1186 ◽  
Author(s):  
R. Baltin
Keyword(s):  
Energy Density ◽  
Density Matrix ◽  
Density Functional ◽  
Particle Density ◽  
Parametric Representation ◽  
Kinetic Energy Density ◽  
Linear Potential ◽  
Energy Density Functional ◽  
The One ◽  
Body Potential

Abstract For a system of independent electrons moving in a common one-body potential V (r) an integral representation of Dirac's density matrix is evaluated in the approximation that V(r) at the point r is replaced by a linear potential with a gradient equal to the gradient of V at r. The particle density ᵨ, ∇ᵨ and the kinetic-energy density εk are derived from the density matrix. After eliminating the potential and its gradient a parametric representation for εk in terms of ᵨ and y = |∇ᵨ |½ ᵨ-⅔ is obtained. Explicit analytical expressions are given in the limits y → 0 and y → ∞ and compared with the inhomogeneity corrections of Kirzhnits and v. Weizsäcker.

scholarly journals Analyticity of the One-Particle Density Matrix

2021 ◽  
Author(s):  
Peter Hearnshaw ◽  
Alexander V. Sobolev
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Real Analytic ◽  
The One ◽  
Coulombic Systems

AbstractIt is proved that the one-particle density matrix $$\gamma (x, y)$$ γ ( x , y ) for multi-particle Coulombic systems is real analytic away from the nuclei and from the diagonal $$x = y$$ x = y .

Static properties of the 2D Hubbard model on a 4×4 cluster

1989 ◽  
Vol 03 (12) ◽  
pp. 1865-1873 ◽  
Author(s):  
Alberto Parola ◽  
Sandro Sorella ◽  
Stefano Baroni ◽  
Michele Parrinello ◽  
Erio Tosatti
Keyword(s):  
Density Matrix ◽  
Hubbard Model ◽  
Particle Density ◽  
Numerical Study ◽  
Exact Diagonalization ◽  
Exact Results ◽  
Power Method ◽  
Static Properties ◽  
Simple Power ◽  
The One

A numerical study of the 2D Hubbard model at various fillings has been performed. The static properties of 10, 14 and 16 electrons on a 4×4 cluster have been studied by exact diagonalization at intermediate couplings. A simple “power method” has been used in order to minimize memory requirements. Spin-spin, charge-charge and hole-hole correlations have been computed together with the one particle density matrix. This computation provides the first exact results on such a system, which can be used as a test for existing simulation algorithms.

Relationships between Jaynes entropy of the one-particle density matrix and Shannon entropy of the electron densities

2002 ◽  
Vol 116 (21) ◽  
pp. 9213-9221 ◽  
Author(s):  
Robin P. Sagar ◽  
Juan Carlos Ramı́rez ◽  
Rodolfo O. Esquivel ◽  
Minhhuy Hô ◽  
Vedene H. Smith
Keyword(s):  
Density Matrix ◽  
Shannon Entropy ◽  
Particle Density ◽  
Electron Densities ◽  
The One
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